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Mastering Trigonometric Functions and Angles for Homework Success

This comprehensive guide covers key concepts in trigonometry, focusing on the functions of acute angles and various angle measurements in degrees and radians. It includes practice problems ranging from basic trigonometric functions to applying the Pythagorean theorem in right triangles. Learn to calculate sine, cosine, and tangent, as well as find missing side lengths and angles. Ideal for students aiming to strengthen their trigonometric understanding and excel in homework assignments.

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Mastering Trigonometric Functions and Angles for Homework Success

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  1. Pg. 323/361 Homework • Pg. 362 #39 – 47 odd, 51, 52Memorize Trig. Info • #2 QIV #4 QIII #6 QIII • #8 -250° #10 470° • #12 338°, 698°, -382°, -742° #14 210°, 570°, -510°, -870° • #16 11π/4, -5π/2 #18 29π/6, -19π/6 • #20 π/4, 9π/4, -15π/4, -23π/4 #22 67°, 157° • #24 78°, 168° #26 5π/12, 11π/12 #28 π/14,4π/7 • #30 90°, π/2 #32 135°, 3π/4 #34 0°, 0, 2π • #36 -120°, -2π/3 #38 -600°, -10π/3 #40 -1260°, -7π • #42 π/3 #44 7π/6 #46 11π/6 • #48 59π/90 #50 249π/180 #52 810/π • #1 #2 #3 8/7 • #4 7/8 #5 #6 • #7 • #8 11/15 #9 #10 • #11 #12 #13 15/11

  2. 6.5 Trig Functions of an Acute Angle Trig Functions Also, we know that from the basic three trig functions: • The six trig functions of any angle 0° < Ɵ < 90° are defined as follows:

  3. 6.5 Trig Functions of an Acute Angle Example: Let Ɵ be an acute angle such that sin Ɵ = 5/6. Find all the trig functions of Ɵ. One angle of a right triangle measures 38°, and the hypotenuse has length of 17. Find the measures of the remaining sides. • They hypotenuse and one leg of a triangle measure 12 and 7 respectively. Find the measure of angle Ɵ formed by these two sides.

  4. 6.5 Trig Functions of an Acute Angle Example: Find the values of all six trig functions and the angle of measure of angle Ɵ, where P(-3, 4) is a point on the terminal side of Ɵ. Find all the values of all six trig functions for the quadrantal angles of: • Find the values of the six trig functions at an angle Ɵ in standard form with point P(4, 7) on its terminal side. • **Note** If an angle does not appear acute in the first quadrant, you can work in any of the four quadrants to make the angle acute!!

  5. 6.5 Trig Functions of an Acute Angle Determining Ɵ • Given the following, find the measure of Ɵ in both degrees and radians.

  6. 6.5 Trig Functions of an Acute Angle Proving. Prove that: • Can you prove that 6•5+2 = 7•5 – 3 • How do you know this? • Prove that:

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